Lexicographically minimal grid path algorithm

It is possible to use string hashing and binary lifting to speed up your current solution, but there is a simpler method.

The minimal string can be built one character at a time, starting from the character at the top left corner.

To get each subsequent character, check the characters to the right and bottom of each of the possible positions of the previous character and eliminate duplicate positions. Then, take the minimum of the characters at all these positions and discard the positions that are not equal to that character for the next iteration.

#include 
#include 
#include 
#include 
#include 
#include 
int main() {
    int n;
    std::cin >> n;
    std::vector grid(n);
    for (auto& row : grid) std::cin >> row;
    std::vector positions{{0, 0}};
    while (!positions.empty()) {
        positions.erase(std::ranges::unique(positions).begin(), positions.end());
        char minc = std::ranges::min(positions | std::views::transform([&](auto& p) { 
            return grid[p.first][p.second];
        }));
        std::cout